PreprintarXiv licencearXiv
Maximum index of unbalanced signed graphs without a positive odd cycle
Abstract
Let πr+ be the set of all balanced signed graphs with underlying graphs Cr. A signed graph is called πr+-free if it contains no subgraph isomorphic to any member of πr+. In this paper, we characterize the extremal graphs that achieve the maximum index among all π2k+1+-free unbalanced signed graphs of order n when kβ₯ 2 and nβ₯ 187k.
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BibTeX
@misc{ma2026maximum,
title = {{Maximum index of unbalanced signed graphs without a positive odd cycle}},
author = {Li Ma and Linfeng Xie and Xiaogang Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15383},
eprint = {2610.15383},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15383},
}
RIS
TY - UNPB
TI - Maximum index of unbalanced signed graphs without a positive odd cycle
AU - Li Ma
AU - Linfeng Xie
AU - Xiaogang Liu
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15383
UR - https://arxiv.org/abs/2610.15383
AB - Let π_r^+ be the set of all balanced signed graphs with underlying graphs C_r. A signed graph is called π_r^+-free if it contains no subgraph isomorphic to any member of π_r^+. In this paper, we characterize the extremal graphs that achieve the maximum index among all π_2k+1^+-free unbalanced signed graphs of order n when kβ₯ 2 and nβ₯ 187k.
ER -